Liouville Classification of Integrable Hamiltonian Systems on Surfaces of Revolution / E. O. Kantonistova. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 5. P. 41-44 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 220-222].

An algorithm for calculation of Fomenko–Zieschang invariants for Hamiltonian systems on 2-dimensional surfaces of revolution is described in the case of the potential V(r)=\cos r. One typical example of such system is considered. Classic examples of systems equivalent to this system in the sense of Liouville are obtained. It is shown that a system studied on a surface of revolution is Liouville equivalent to a geodesic flow on this surface.

Key words: integrable Hamiltonian system, Liouville fibration, Fomenko–Zieschang invariant, marked molecule.